implement is_prime() for ideals

[aghitza]

The attached patch implements a generic primality testing method for ideals. It is based on the computation of the associated primes of an ideal, and so at the moment will only work for ideals that have this implemented (e.g. ideals in multivariate polynomial rings that Singular can handle).

There are also a few related methods such as is_primary() and embedded_primes().

Component: commutative algebra

Keywords: prime ideal

Author: Alex Ghitza

Reviewer: Martin Albrecht

Merged: sage-4.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7450

[malb]

comment:1

• patch applies cleanly against 4.2
  • doctests pass
  • reference manual builds without reporting any issues
  • note that there are macros for citations available in ReST: http://sphinx.pocoo.org/rest.html#citations

Other than the last nitpick the patch looks fine.

[aghitza]

comment:2

Aha! Thanks for the pointer for citations. I had looked in the developer guide and there was nothing about this (I'll open a new ticket to fix that).

I have replaced the patch with one that has the proper citation markup. Having had a look at the html output, I also fixed the markup for apply_morphism.

[aghitza]

comment:3

Attachment: trac_7450.patch.gz

And I replaced it once more, having added an optional argument to is_primary to check whether an ideal is primary wrt a given prime ideal; also added more doctests borrowed from the Macaulay2 docs.

[malb]

comment:4

Looks good.

[mwhansen]

Reviewer: Martin Albrecht